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University of Sydney Algebra Seminar

Jiuzu Hong

Friday 21 February, 12-1pm, in the SMRI Seminar room (McLeay Building A12, Room 301)

A comparison theorem for affine Demazure modules

Given an integrable highest weight representation $L(\mathrm{\Lambda })$ of an affine Lie algebra $\hat{g}$ associated to a simple Lie algebra $g$, we consider a summation of certain affine Demazure modules in $L(\mathrm{\Lambda })$. We show that the character of this summation with respect to the Cartan subalgebra $h$ of $g$, up to a shift of $\mathrm{\Lambda }$ restricted to $h$, is dependent only on the level of $L(\mathrm{\Lambda })$. This result refines the coherence conjecture by Pappas-Rapoport, which was proven by Zhu and focuses on comparing dimensions. To establish this comparison theorem, we investigate line bundles on global Schubert varieties of parahoric Bruhat-Tits group schemes and equip them with certain equivariant structures. This talk will be based on a joint work with Huanhuan Yu.